Finite Group Databasebeta

← C151×#18994 #50323919

Subgroups — C151×#18994 #50323919

Order 38656.

936 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#563×C151C211yesmaximal, characteristic, complemented
2#3234×C151C212yesmaximal, complemented
3#3153×C151C211yesmaximal, characteristic
4#1660×C151C214yesmaximal, complemented
5#1657×C151C214yesmaximal, complemented
6#1533×C151C211yesmaximal, characteristic, complemented
7#1528×C151C212yesmaximal, complemented
8C2×#137×C151—21no—
9C2×AGL(1,ℤ/8)×C151—21no—
10#563×C151—24no—
11#563×C151—22no—
12#563×C151C2214yes—
13#532×C151C2211yescharacteristic
14C2×C4⋊Q8×C151—21no—
15C2×#126×C151—22no—
16C2×#125×C151C2212yes—
17C2×#124×C151C2211yescharacteristic
18C2×#123×C151—21no—
19C2×C22⋊Q8×C151—22no—
20#501×C151C2214yescomplemented
21#497×C151C2212yes—
22#496×C151C2212yes—
23#495×C151—22no—
24#490×C151C2214yescomplemented
25#481×C151—22no—
26#480×C151—22no—
27#478×C151—24no—
28#432×C151C2212yes—
29C4×M16×C151C2211yescharacteristic
30#330×C151C2218yescomplemented
31#329×C151C2214yes—
32C2×#41×C151—21no—
33C22×Q8×C151—21no—
34C22×Q8×C151D411yescharacteristic
35C22×D4×C151D411yescharacteristic
36C23×C4×C151—21no—
37#137×C151—44no—
38AGL(1,ℤ/8)×C151—44no—
39C2×Q16×C151—22no—
40C2×SD16×C151—22no—
41C2×SD16×C151—22no—
42C2×D8×C151—22no—
43C2×M16×C151—21no—
44C4⋊Q8×C151—24no—
45C4⋊Q8×C151—24no—
46C4⋊Q8×C151C2311yescharacteristic
47#127×C151C2311yescharacteristic
48#126×C151—28no—
49#126×C151—28no—
50#125×C151—22no—
51#125×C151—22no—
52#125×C151D414yes—
53#125×C151C2314yes—
54#124×C151—22no—
55#124×C151—21no—
56#124×C151D412yes—
57#124×C151C2312yes—
58#123×C151—24no—
59#123×C151—24no—
60C22⋊Q8×C151—28no—
61C22⋊Q8×C151—28no—
62#121×C151—22no—
63C4×D4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151D412yes—
68C2×C4⋊C4×C151D412yes—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—22no—
72C2×C42×C151—21no—
73C2×C42×C151C2311yescharacteristic
74#107×C151—24no—
75#106×C151—24no—
76C4⋊C8×C151—22no—
77#102×C151—24no—
78#102×C151—24no—
79C22⋊C8×C151—22no—
80#97×C151C2312yes—
81#97×C151C2314yes—
82C4×C8×C151—21no—
83C24×C151—21no—
84#41×C151—42no—
85#41×C151—42no—
86C2×Q8×C151—24no—
87C2×Q8×C151—21no—
88C2×Q8×C151—21no—
89C2×Q8×C151—42no—
90C2×Q8×C151—82no—
91C2×Q8×C151C2×D412yes—
92C2×D4×C151—21no—
93C2×D4×C151—22no—
94C2×D4×C151—21no—
95C2×D4×C151—42no—
96C2×D4×C151—41no—
97C2×D4×C151C2×D412yes—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—24no—
102C22×C4×C151—41no—
103C22×C4×C151—82no—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2×D412yes—
106Q16×C151—44no—
107SD16×C151—44no—
108SD16×C151—44no—
109D8×C151—44no—
110M16×C151—24no—
111C2×C8×C151—22no—
112C2×C8×C151—24no—
113C4⋊C4×C151—28no—
114C4⋊C4×C151—24no—
115C4⋊C4×C151—24no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—24no—
119C4⋊C4×C151—24no—
120C4⋊C4×C151—22no—
121C4⋊C4×C151C2×D414yes—
122C4⋊C4×C151C2×D414yes—
123C22⋊C4×C151—28no—
124C22⋊C4×C151—24no—
125C22⋊C4×C151—24no—
126C22⋊C4×C151—24no—
127C22⋊C4×C151—42no—
128C42×C151—24no—
129C42×C151C2×D411yescharacteristic
130C42×C151C2×D412yes—
131C42×C151C2411yescharacteristic
132C23×C151—22no—
133C23×C151—44no—
134C23×C151—42no—
135C23×C151—41no—
136C23×C151#12011yescharacteristic
137Q8×C151—42no—
138Q8×C151—41no—
139Q8×C151—41no—
140Q8×C151—81no—
141Q8×C151—84no—
142D4×C151—42no—
143D4×C151—41no—
144D4×C151—41no—
145D4×C151—44no—
146D4×C151—81no—
147D4×C151—82no—
148C2×C4×C151—22no—
149C2×C4×C151—22no—
150C2×C4×C151—24no—
151C2×C4×C151—24no—
152C2×C4×C151—42no—
153C2×C4×C151—44no—
154C2×C4×C151—42no—
155C2×C4×C151—44no—
156C2×C4×C151—41no—
157C2×C4×C151—82no—
158C2×C4×C151—84no—
159C2×C4×C151#12011yescharacteristic
160C2×C4×C151#12012yes—
161C2×C4×C151C22×D411yescharacteristic
162C2×C4×C151C22×D412yes—
163C8×C151—24no—
164C8×C151—44no—
165C22×C151—22no—
166C22×C151—42no—
167C22×C151—44no—
168C22×C151—84no—
169C22×C151—81no—
170C22×C151—82no—
171C22×C151#45312yes—
172C22×C151C2×#12011yescharacteristic
173C4×C151—21no—
174C4×C151—21no—
175C4×C151—22no—
176C4×C151—22no—
177C4×C151—44no—
178C4×C151—42no—
179C4×C151—44no—
180C4×C151—81no—
181C2×C151—22no—
182C2×C151—82no—
183C2×C151—161no—
184C2×C151C2×#45311yescharacteristic
185C2×C151#302012yes—
186#18994C15111yesmaximal, characteristic, direct product factor, Sylow
187C151#1899411yescharacteristic, direct product factor, Sylow
188C2×#563C2×C15111yescharacteristic, complemented
189#3234C2×C15112yescomplemented
190#3153C2×C15111yescharacteristic
191#1660C2×C15114yescomplemented
192#1657C2×C15114yescomplemented
193#1533C2×C15111yescharacteristic, complemented
194#1528C2×C15112yescomplemented
195C2×#137—21no—
196C2×AGL(1,ℤ/8)—21no—
197#563—24no—
198#563—22no—
199#563C22×C15114yes—
200#532C22×C15111yescharacteristic
201C2×C4⋊Q8—21no—
202C2×#126—22no—
203C2×#125C22×C15112yes—
204C2×#124C22×C15111yescharacteristic
205C2×#123—21no—
206C2×C22⋊Q8—22no—
207#501C22×C15114yescomplemented
208#497C22×C15112yes—
209#496C22×C15112yes—
210#495—22no—
211#490C22×C15114yescomplemented
212#481—22no—
213#480—22no—
214#478—24no—
215#432C22×C15112yes—
216C4×M16C22×C15111yescharacteristic
217#330C22×C15118yescomplemented
218#329C22×C15114yes—
219C2×#41—21no—
220C22×Q8—21no—
221C22×Q8D4×C15111yescharacteristic
222C22×D4D4×C15111yescharacteristic
223C23×C4—21no—
224#137—44no—
225AGL(1,ℤ/8)—44no—
226C2×Q16—22no—
227C2×SD16—22no—
228C2×SD16—22no—
229C2×D8—22no—
230C2×M16—21no—
231C4⋊Q8—24no—
232C4⋊Q8—24no—
233C4⋊Q8C23×C15111yescharacteristic
234#127C23×C15111yescharacteristic
235#126—28no—
236#126—28no—
237#125—22no—
238#125—22no—
239#125D4×C15114yes—
240#125C23×C15114yes—
241#124—22no—
242#124—21no—
243#124D4×C15112yes—
244#124C23×C15112yes—
245#123—24no—
246#123—24no—
247C22⋊Q8—28no—
248C22⋊Q8—28no—
249#121—22no—
250C4×D4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4D4×C15112yes—
255C2×C4⋊C4D4×C15112yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C42—21no—
260C2×C42C23×C15111yescharacteristic
261#107—24no—
262#106—24no—
263C4⋊C8—22no—
264#102—24no—
265#102—24no—
266C22⋊C8—22no—
267#97C23×C15114yes—
268#97C23×C15112yes—
269C4×C8—21no—
270C24—21no—
271#41—42no—
272#41—42no—
273C2×Q8—24no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—42no—
277C2×Q8—82no—
278C2×Q8C2×D4×C15112yes—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—42no—
283C2×D4—41no—
284C2×D4C2×D4×C15112yes—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—41no—
290C22×C4—82no—
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×D4×C15112yes—
293Q16—44no—
294SD16—44no—
295SD16—44no—
296D8—44no—
297M16—24no—
298C2×C8—22no—
299C2×C8—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4C2×D4×C15114yes—
309C4⋊C4C2×D4×C15114yes—
310C22⋊C4—28no—
311C22⋊C4—24no—
312C22⋊C4—24no—
313C22⋊C4—24no—
314C22⋊C4—42no—
315C42—24no—
316C42C2×D4×C15111yescharacteristic
317C42C2×D4×C15112yes—
318C42C24×C15111yescharacteristic
319C23—22no—
320C23—44no—
321C23—42no—
322C23—41no—
323C23#120×C15111yescharacteristic
324Q8—42no—
325Q8—41no—
326Q8—41no—
327Q8—81no—
328Q8—84no—
329D4—42no—
330D4—41no—
331D4—41no—
332D4—44no—
333D4—81no—
334D4—82no—
335C2×C4—22no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—84no—
346C2×C4#120×C15112yes—
347C2×C4#120×C15111yescharacteristic
348C2×C4C22×D4×C15112yes—
349C2×C4C22×D4×C15111yescharacteristic
350C8—24no—
351C8—44no—
352C22—22no—
353C22—42no—
354C22—44no—
355C22—84no—
356C22—81no—
357C22—82no—
358C22#453×C15112yes—
359C22C2×#120×C15111yescharacteristic
360C4—21no—
361C4—21no—
362C4—22no—
363C4—22no—
364C4—44no—
365C4—42no—
366C4—44no—
367C4—81no—
368C2—22no—
369C2—82no—
370C2—161no—
371C2C2×#453×C15111yescharacteristic
372C2#3020×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3153×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#563×C151C2semidirect
2. #3234×C151C2semidirect
4. #1660×C151C2semidirect
5. #1657×C151C2semidirect
6. #1533×C151C2semidirect
7. #1528×C151C2semidirect
20. #501×C151C22semidirect
24. #490×C151C22semidirect
30. #330×C151C22semidirect
186. #18994C151direct (N × H)
187. C151#18994direct (N × H)
188. C2×#563C2×C151semidirect
189. #3234C2×C151semidirect
191. #1660C2×C151semidirect
192. #1657C2×C151semidirect
193. #1533C2×C151semidirect
194. #1528C2×C151semidirect
207. #501C22×C151semidirect
211. #490C22×C151semidirect
217. #330C22×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#563×C1512
#3234×C1512
#3153×C1512
#1660×C1512
#1657×C1512
#1533×C1512
#1528×C1512
#18994151